Neutron Star Equation Of State Research Articles

Neutron star equations of state and their applications

This paper reviews the properties of neutron stars based on the recent multi-messenger observations including electromagnetic waves from the low-mass X-ray binaries and gravitational waves from the merger of neutron star binaries. Based on these observations, we investigate theoretical models for dense nuclear matter and discuss their implications to the neutron star observations such as mass, radius, cooling, and tidal deformability. We also discuss the uncertainties in the neutron star cooling, neutron star properties with Bayesian approaches, and an expansion scheme applied to the nuclear energy density functional theory.

Effect of free parametrized TOV on properties of neutron stars

Recently, much progress has been reported about the properties of neutron stars (NS). However, in some parts such radius and moment of Inertia of NSs are still uncertain. We are interested in studying the properties of neutron stars also by using free parametric constraints. In this work, we use the modified Tolman Oppenheimer Volkoff (TOV) equation known as the parameterization of TOV (PTOV). Relativistic Mean Field (RMF) model is used to calculate the equation of state (EoS) of an NS. NS EoS is used as input to calculate some properties of NSs. The properties of neutron stars that are the focus of this research is mass, radius, and moment of inertia of slowly rotating NSs. We observe the effect of each free parameter added to the TOV equation, which results in a shift from the mass-radius diagram. We obtain the results which are consistent with the constraint of maximum mass M < 2.35 M⊙ and constraint of radius 11.38 < R1.4M⊙ (km) < 13.77. We observe that the contribution of each free parameter can increase mass and decrease the radii as well as provide an impact on the corresponding moment of inertia.

Inferring the dense nuclear matter equation of state with neutron star tides

AbstractDuring the late stages of a neutron star binary inspiral finite-size effects come into play, with the tidal deformability of the supranuclear density matter leaving an imprint on the gravitational-wave signal. As demonstrated in the case of GW170817—the first direct detection of gravitational waves from a neutron star binary—this can lead to strong constraints on the neutron star equation of state. As detectors become more sensitive, effects which may have a smaller influence on the neutron star tidal deformability need to be taken into consideration. Dynamical effects, such as oscillation mode resonances triggered by the orbital motion, have been shown to contribute to the tidal deformability, especially close to the neutron star coalesence. We calculate the contribution of the various stellar oscillation modes to the tidal deformability and demonstrate the (anticipated) dominance of the fundamental mode, showing what the impact of the matter composition is on the tidal deformability.

Cooling of dark-matter admixed neutron stars with density-dependent equation of state

We propose a dark-matter (DM) admixed density-dependent equation of state where the fermionic DM interacts with the nucleons via Higgs portal. Presence of DM can hardly influence the particle distribution inside neutron star (NS) but can significantly affect the structure as well as equation of state (EOS) of NS. Introduction of DM inside NS softens the equation of state. We explored the effect of variation of DM mass and DM Fermi momentum on the NS EOS. Moreover, DM-Higgs coupling is constrained using dark matter direct detection experiments. Then, we studied cooling of normal NSs using APR and DD2 EOSs and DM admixed NSs using dark-matter modified DD2 with varying DM mass and Fermi momentum. We have done our analysis by considering different NS masses. Also DM mass and DM Fermi momentum are varied for fixed NS mass and DM-Higgs coupling. We calculated the variations of luminosity and temperature of NS with time for all EOSs considered in our work and then compared our calculations with the observed astronomical cooling data of pulsars namely Cas A, RX J0822-43, 1E 1207-52, RX J0002+62, XMMU J17328, PSR B1706-44, Vela, PSR B2334+61, PSR B0656+14, Geminga, PSR B1055-52 and RX J0720.4-3125. It is found that APR EOS agrees well with the pulsar data for lighter and medium mass NSs but cooling is very fast for heavier NS. For DM admixed DD2 EOS, it is found that for all considered NS masses, all chosen DM masses and Fermi momenta agree well with the observational data of PSR B0656+14, Geminga, Vela, PSR B1706-44 and PSR B2334+61. Cooling becomes faster as compared to normal NSs in case of increasing DM mass and Fermi momenta. It is infered from the calculations that if low mass super cold NSs are observed in future that may support the fact that heavier WIMP can be present inside neutron stars.

Neutron star equation of state and tidal deformability with nuclear energy density functionals

Neutron star is the ultimate testing place for the physics of dense nuclear matter. Before the detection of gravitational waves from the merger of binary neutron stars, various nuclear equations of state have been used to estimate the macroscopic properties of neutron stars, such as masses and radii, based on the electromagnetic observations. However, recent observations on the tidal deformability of neutron star from the gravitational waves GW170817 opened a new era of multi-messenger astronomy and astrophysics, and many theoretical works have been extended to estimate the tidal deformability of neutron stars. In this article, we review our recent works on the application of nuclear energy density functionals to the properties of neutron stars including tidal deformability. We found that many nuclear energy density functionals, including new KIDS (Korea: IBS-Daegu-Sungkyunkwan) model, satisfy both constraints from current electromagnetic and gravitational wave observations. We discuss future possibilities of constraining nuclear matter equation of state from ground-based experiments and multi-messenger observations.

Constraints on neutron stars equation of state using the tidal deformability derived from BNS mergers

The purpose of this work is the study of neutron stars (NS) equation of state (EOS) using constraints on tidal deformability derived from observation of binary neutron star (BNS) mergers, such as GW170817. The mathematical formalism is introduced, and then for a variety of EOS the system is solved numerically, allowing us to determine the mass, the radius, the tidal love number and the tidal deformability of the NS, each one of them unique for each EOS. Moreover, for a fixed value of chirp mass under the assumption that m2&lt;m1 (where m1 is the heavier component mass of BNS system), the effective (mass-weighted) tidal deformability of the binary system is determined for each EOS. We consider both an upper limit (GW170817) and a lower limit (AT2017gfo) for the effective tidal deformability. Also, we construct the Λ1-Λ2 space and we compare the behavior of EOS with the most recent LIGO’s data. We found out that the most EOS models give values for the effective tidal deformability less than the upper limit and that the most stiff EOS are excluded.

What Constraints on the Neutron Star Maximum Mass Can One Pose from GW170817 Observations?

Abstract The post-merger product of the first binary neutron star merger event detected in gravitational waves, GW170817, depends on neutron star equation of state (EoS) and is not well determined. We generally discuss the constraints one may pose on the maximum mass of a non-spinning neutron star, M TOV, based on the observations and some EoS-independent universal relations of rapidly spinning neutron stars. If the merger product is a black hole after a brief hypermassive neutron star (HMNS) phase, we derive at the 2σ (1σ) level. The cases for a massive neutron star (MNS), neither a supramassive neutron star (SMNS) nor even a stable neutron star (SNS) are also allowed by the data. We derive for the SMNS case and for the SNS case, at the 2σ (1σ) confidence level. In the MNS cases, we also discuss the constraints on the neutron star parameters (the dipolar magnetic field strength at the surface B p and the ellipticity ϵ) that affect the spin down history, by considering different MNS survival times, e.g., 300 s, 1 day, and 155 days after the merger, as suggested by various observational arguments. We find that once an SMNS is formed, without violating the electromagnetic observational constraints, there always exist a set of ( ) parameters that allow the SMNS to survive for 300 s, 1 day, 155 days, or even longer.

Gravitational waves or deconfined quarks: What causes the premature collapse of neutron stars born in short gamma-ray bursts?

We infer the collapse times of long-lived neutron stars into black holes using the X-ray afterglows of 18 short gamma-ray bursts. We then apply hierarchical inference to infer properties of the neutron star equation of state and dominant spin-down mechanism. We measure the maximum non-rotating neutron star mass $M_\mathrm{TOV} = 2.31 ^{+0.36}_{-0.21} M_{\odot}$ and constrain the fraction of remnants spinning down predominantly through gravitational-wave emission to $\eta = 0.69 ^{+0.21}_{-0.39}$ with $68 \%$ uncertainties. In principle, this method can determine the difference between hadronic and quark equation of states. In practice, however, the data is not yet informative with indications that these neutron stars do not have hadronic equation of states at the $1\sigma$ level. These inferences all depend on the underlying progenitor mass distribution for short gamma-ray bursts produced by binary neutron star mergers. The recently announced gravitational-wave detection of GW190425 suggests this underlying distribution is different from the locally-measured population of double neutron stars. We show that $M_\mathrm{TOV}$ and $\eta$ constraints depend on the fraction of binary mergers that form through a distribution consistent with the locally-measured population and a distribution that can explain GW190425. The more binaries that form from the latter distribution, the larger $M_\mathrm{TOV}$ needs to be to satisfy the X-ray observations. Our measurements above are marginalised over this unknown fraction. If instead, we assume GW190425 is not a binary neutron star merger, i.e the underlying mass distribution of double neutron stars is the same as observed locally, we measure $M_\mathrm{TOV} = 2.26 ^{+0.31}_{-0.17} M_{\odot}$.

Quantum enhanced kHz gravitational wave detector with internal squeezing

We propose adding a nonlinear element to a long signal recycling cavity to enhance the high-frequency sensitivity (900 Hz–5 kHz) of a kilometer-scale interferometric gravitational wave detector. Using numbers for absorption and scattering losses in the detector consistent with advanced LIGO+, we demonstrate a factor of 3.5 improvement in quantum noise limited strain sensitivity in the kHz regime. Such a configuration is robust to internal losses and reduces the requirement on the amount of circulating power in the detector to achieve sensitivity comparable to future gravitational wave detectors. This proposed configuration is compatible with the existing gravitational wave detector vacuum infrastructure and could enable exploration of exotic science, such as observing the merger phase of binary neutron stars, which in turn may provide constraints on the neutron star equation of state.

Ultrarelativistic astrophysics using multimessenger observations of double neutron stars with LISA and the SKA

ABSTRACTRecent work highlights that tens of Galactic double neutron stars are likely to be detectable in the millihertz band of the space-based gravitational-wave observatory, LISA, some of which might be detectable as radio pulsars using the Square Kilometer Array (SKA). We point out that the joint LISA + SKA detection of a fgw ≳ 1 mHz binary, corresponding to a binary period of ≲400 s, would enable precision measurements of ultrarelativistic phenomena. We show that, given plausible assumptions, multimessenger observations of ultrarelativistic binaries can be used to constrain the neutron star equation of state with remarkable fidelity. It may be possible to measure the mass–radius relation with a precision of ≈0.2 per cent after 10 yr of observations with the SKA. Such a measurement would be roughly an order of magnitude more precise than possible with other proposed observations. We summarize some of the other remarkable science made possible with multimessenger observations of millihertz binaries, and discuss the prospects for the detection of such objects.

Studying strong phase transitions in neutron stars with gravitational waves

The composition of neutron stars at the extreme densities reached in their cores is currently unknown. Besides nuclear matter of normal neutrons and protons, the cores of neutron stars might harbor exotic matter such as deconfined quarks. In this paper we study strong hadron-quark phase transitions in the context of gravitational wave observations of inspiraling neutron stars. We consider upcoming detections of neutron star coalescences and model the neutron star equations of state with phase transitions through the Constant-Speed-of-Sound parametrization. We use the fact that neutron star binaries with one or more hadron-quark hybrid stars can exhibit qualitatively different tidal properties than binaries with hadronic stars of the same mass, and hierarchically model the masses and tidal properties of simulated populations of binary neutron star inspiral signals. We explore the parameter space of phase transitions and discuss under which conditions future observations of binary neutron star inspirals can identify this effect and constrain its properties, in particular the threshold density at which the transition happens and the strength of the transition. We find that if the detected population of binary neutron stars contains both hadronic and hybrid stars, the onset mass and strength of a sufficiently strong phase transition can be constrained with 50-100 detections. If the detected neutron stars are exclusively hadronic or hybrid, then it is possible to place lower or upper limits on the transition density and strength.

Model comparison from LIGO–Virgo data on GW170817’s binary components and consequences for the merger remnant

GW170817 is the very first observation of gravitational waves originating from the coalescence of two compact objects in the mass range of neutron stars, accompanied by electromagnetic counterparts, and offers an opportunity to directly probe the internal structure of neutron stars. We perform Bayesian model selection on a wide range of theoretical predictions for the neutron star equation of state. For the binary neutron star hypothesis, we find that we cannot rule out the majority of theoretical models considered. In addition, the gravitational-wave data alone does not rule out the possibility that one or both objects were low-mass black holes. We discuss the possible outcomes in the case of a binary neutron star merger, finding that all scenarios from prompt collapse to long-lived or even stable remnants are possible. For long-lived remnants, we place an upper limit of 1.9 kHz on the rotation rate. If a black hole was formed any time after merger and the coalescing stars were slowly rotating, then the maximum baryonic mass of non-rotating neutron stars is at most , and three equations of state considered here can be ruled out. We obtain a tighter limit of for the case that the merger results in a hypermassive neutron star.

Neutron Star Extreme Matter Observatory: A kilohertz-band gravitational-wave detector in the global network

Abstract Gravitational waves from coalescing neutron stars encode information about nuclear matter at extreme densities, inaccessible by laboratory experiments. The late inspiral is influenced by the presence of tides, which depend on the neutron star equation of state. Neutron star mergers are expected to often produce rapidly rotating remnant neutron stars that emit gravitational waves. These will provide clues to the extremely hot post-merger environment. This signature of nuclear matter in gravitational waves contains most information in the 2–4 kHz frequency band, which is outside of the most sensitive band of current detectors. We present the design concept and science case for a Neutron Star Extreme Matter Observatory (NEMO): a gravitational-wave interferometer optimised to study nuclear physics with merging neutron stars. The concept uses high-circulating laser power, quantum squeezing, and a detector topology specifically designed to achieve the high-frequency sensitivity necessary to probe nuclear matter using gravitational waves. Above 1 kHz, the proposed strain sensitivity is comparable to full third-generation detectors at a fraction of the cost. Such sensitivity changes expected event rates for detection of post-merger remnants from approximately one per few decades with two A+ detectors to a few per year and potentially allow for the first gravitational-wave observations of supernovae, isolated neutron stars, and other exotica.

Measuring the neutron star equation of state with gravitational waves: The first forty binary neutron star merger observations

Gravitational waves from binary neutron star coalescences contain rich information about matter at supranuclear densities encoded by the neutron star equation of state. We can measure the equation of state by analyzing the tidal interactions between neutron stars, which is quantified by the tidal deformability. Multiple merger events are required to probe the equation of state over a range of neutron star masses. The more events included in the analysis, the stronger the constraints on the equation of state. In this paper, we build on previous work to explore the constraints that LIGO and Virgo are likely to place on the neutron star equation of state by combining the first 40 binary neutron star detections, a milestone we project to be reached during the first year of accumulated design-sensitivity data. We carry out Bayesian inference on a realistic mock dataset of binaries to obtain posterior distributions for neutron star tidal parameters. In order to combine posterior samples from multiple observations, we employ a random forest regressor, which allows us to efficiently interpolate the likelihood distribution. Assuming a merger rate of $1540\text{ }\text{ }{\mathrm{Gpc}}^{\ensuremath{-}3}\text{ }\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$ and a LIGO-Virgo detector network operating for 1 year at the sensitivity of the third-observation run, plus an additional 8 months of design sensitivity, we find that the radius of a $1.4\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ neutron star can be constrained to better than $\ensuremath{\sim}10%$ at 90% confidence. The pressure at twice the nuclear saturation density can be constrained to better than $\ensuremath{\sim}45%$ at 90% confidence. We show that these results are robust to our choice of parametrization for the neutron star equation of state.

Bayesian modeling of the nuclear equation of state for neutron star tidal deformabilities and GW170817

We present predictions for neutron star tidal deformabilities obtained from a Bayesian analysis of the nuclear equation of state, assuming a minimal model at high-density that neglects the possibility of phase transitions. The Bayesian posterior probability distribution is constructed from priors obtained from microscopic many-body theory based on realistic two- and three-body nuclear forces, while the likelihood functions incorporate empirical information about the equation of state from nuclear experiments. The neutron star crust equation of state is constructed from the liquid drop model, and the core-crust transition density is found by comparing the energy per baryon in inhomogeneous matter and uniform nuclear matter. From the cold $\beta$-equilibrated neutron star equation of state, we then compute neutron star tidal deformabilities as well as the mass-radius relationship. Finally, we investigate correlations between the neutron star tidal deformability and properties of finite nuclei.

New Neutron Star Equation of State with Quark–Hadron Crossover

Abstract We present a much improved equation of state for neutron star matter, QHC19, with a smooth crossover from the hadronic regime at lower densities to the quark regime at higher densities. We now use the Togashi et al. equation of state, a generalization of the Akmal–Pandharipande–Ravenhall equation of state of uniform nuclear matter, in the entire hadronic regime; the Togashi equation of state consistently describes nonuniform as well as uniform matter, and matter at beta equilibrium without the need for an interpolation between pure neutron and symmetric nuclear matter. We describe the quark matter regime at higher densities with the Nambu–Jona–Lasinio model, now identifying tight constraints on the phenomenological universal vector repulsion between quarks and the pairing interaction between quarks arising from the requirements of thermodynamic stability and causal propagation of sound. The resultant neutron star properties agree very well with the inferences of the LIGO/Virgo collaboration, from GW170817, of the pressure versus baryon density, neutron star radii, and tidal deformabilities. The maximum neutron star mass allowed by QHC19 is 2.35 M ⊙, consistent with all neutron star mass determinations.

Constraining the Neutron Star Equation of State Using Multiband Independent Measurements of Radii and Tidal Deformabilities.

Using a Bayesian approach, we combine measurements of neutron star macroscopic observables obtained by astrophysical and gravitational observations to derive joint constraints on the equation of state (EOS) of matter at supranuclear density. In our analysis, we use two sets of data: (i)the masses and tidal deformabilities measured in the binary neutron star event GW170817, detected by LIGO and Virgo, and (ii)the masses and stellar radii measured from observations of nuclear bursts in accreting low-mass x-ray binaries. Using a phenomenological parametrization of the equation of state, we compute the posterior probability distributions of the EOS parameters, using which we infer the posterior distribution for the radius and the mass of the two neutron stars of GW170817. The constraints we set on the radii are tighter than previous bounds.

Inspiralling eccentric binary neutron stars: Orbital motion and tidal resonance

We study the orbital evolution of eccentric binary neutron stars. The orbit is described as a Quasi-Keplarian orbit with perturbations due to tidal couplings. We find that the tidal interaction between stars contributes to orbital precession, in addition to the Post-Newtonian procession. The coupling between the angular and radial motion of the binary also excites a series of harmonics in the stars' oscillation. In the small eccentricity limit, this coupling mainly gives rise to an additional orbital resonance, with the orbital frequency being one third of the f-mode frequency. For a binary with initial eccentricity $\sim 0.2$ at $50$Hz orbital frequency, the presence of this tidal resonance introduces $\sim 0.5$ phase shift in the gravitational waveform till merger, subject to uncertainties in neutron star equation of state and the distribution of binary component masses. Such phase shift in the late-inspiral stage is likely detectable with third-generation gravitational-wave detectors.

Parallelized inference for gravitational-wave astronomy

Bayesian inference is the workhorse of gravitational-wave astronomy, for example, determining the mass and spins of merging black holes, revealing the neutron star equation of state, and unveiling the population properties of compact binaries. The science enabled by these inferences comes with a computational cost that can limit the questions we are able to answer. This cost is expected to grow. As detectors improve, the detection rate will go up, allowing less time to analyze each event. Improvement in low-frequency sensitivity will yield longer signals, increasing the number of computations per event. The growing number of entries in the transient catalog will drive up the cost of population studies. While Bayesian inference calculations are not entirely parallelizable, key components are embarrassingly parallel: calculating the gravitational waveform and evaluating the likelihood function. Graphical processor units (GPUs) are adept at such parallel calculations. We report on progress porting gravitational-wave inference calculations to GPUs. Using a single code - which takes advantage of GPU architecture if it is available - we compare computation times using modern GPUs (NVIDIA P100) and CPUs (Intel Gold 6140). We demonstrate speed-ups of $\sim 50 \times$ for compact binary coalescence gravitational waveform generation and likelihood evaluation and more than $100\times$ for population inference within the lifetime of current detectors. Further improvement is likely with continued development. Our python-based code is publicly available and can be used without familiarity with the parallel computing platform, CUDA.

Accelerated detection of the binary neutron star gravitational-wave background

Most gravitational-wave signals from binary neutron star coalescences are too weak to be individually resolved with current detectors. We demonstrate how to extract a population of sub-threshold binary neutron star signals using Bayesian parameter estimation. Assuming a merger rate of one signal every two hours, we find that this gravitational-wave background can be detected after approximately three months of observation with Advanced LIGO and Virgo at design sensitivity, versus several years using the standard cross-correlation algorithm. We show that the algorithm can distinguish different neutron star equations of state using roughly seven months of Advanced LIGO and Virgo design-sensitivity data. This is in contrast to the standard cross-correlation method, which cannot.